Higher order theories for the free vibration analysis of laminated anisotropic doubly-curved shells of arbitrary geometry with general boundary conditions

The present work investigates the modal response of doubly-curved shells characterized by unsymmetric lamination schemes embedding anisotropic materials and externally constrained with general boundary conditions along the edges. The Equivalent Single Layer (ESL) methodology has been adopted for the assessment of the fundamental governing equations, employing a generalized formulation for the setup of each component of the kinematic field variable, leading to a higher order through-the-thickness expression of the displacement field. A two-dimensional non uniform discrete grid has been sat up within the mapped physical domain. The fundamental equations have been derived from the Hamiltonian Principle, and the problem has been solved employing a weak formulation of the field variable based on a higher order Lagrange polynomials-based interpolation algorithm. General boundary conditions have been obtained starting from a series of translational springs for each principal direction of the shell, each of them distributed following a generalized analytical expression. After some validations with respect to refined three-dimensional models, a systematic analysis has been performed, where the mode frequencies and shapes of structures with different syngonies and curvatures have been investigated. It has been shown that the modal response of anisotropic doubly-curved shells can be significantly oriented if governing distribution parameters are correctly selected.